Well I guess doing symbolic computation in a clean fashion is never easy ...
I'm not unfimiliar with the notion of Picard-Vessiot extensions, but I will have a second look into it. Thanks for the input. On Friday, December 20, 2013 8:19:33 PM UTC+1, Nils Bruin wrote: > > On Friday, December 20, 2013 2:58:51 AM UTC-10, maldun wrote: >> >> Another more careful approach would be to start at the field of rational >> functions and extend it step by step with algebraic and transcendental >> functions, till we reach a field which is maximal under the available >> symbolic expressions. >> > I hope you realize that you're going through the same steps as the > mathematicians who have been involved in developing axiom, macsyma, maple, > mathematica etc. before they settled for the mess that we have now? It may > well be possible to come up with a better way of dealing with things, but > you'll probably need a fundamentally new computational/representational > insight to get it. And you'll probably not get something that is more > appealing to beginners than the apparent simplicity of the pen-and-paper > approach that SR takes to representing its elements (at least not at first). > > If you're interested in taking an algebraic approach to the functions that > arise from ordinary linear differential equations (and that includes a lot > of the functions relevant for calculus) you should read up on > Picard-Vessiot extensions. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
